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Just a note
This is the standard normal distribution, whose intimate details are to be found in any book of statistical tables. Because it's 'tails' are infinitely long, we cannot show all of this monster  but it is obviously smooth and symmetrical.
This figure shows two ways of graphing this distribution  as a bellshaped 'density function', or as an sshaped 'cumulative function'. Notice that the highest point on the bell shaped curve is equivalent to the 'point of inflection' of the sshaped curve  in other words, where the cumulative function stops curving upwards, and starts to curve in the opposite direction. This point is the mean, median and mode. The bellshaped curve has two points of inflection, both of which lie one standard deviation from the mean  although we have only labelled one of these points.
